Analogs of quantum Hall effect edge states in photonic crystals

Abstract

"Photonic crystals" built with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries across which the Faraday axis reverses. These modes are precise analogs of the electronic edge states of quantum Hall effect (QHE) systems, and are also immune to backscattering and localization by disorder. The "Berry curvature" of the photonic bands plays a role analogous to that of the magnetic field in the QHE. Explicit calculations demonstrating the existence of such unidirectionally-propagating photonic edge states are presented.

23 pages, 19 figures

Cited by in corpus (226)

• Topological Photonics
• Quantum fluids of light
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Chiral Quantum Optics
• Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Topological properties of linear circuit lattices
• Topological photonic crystals: physics, designs and applications
• Topological Polaritons
• Do Linear Dispersions of Classical Waves Mean Dirac Cones?
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Active topological photonics
• Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides
• Crystalline metamaterials for topological properties at subwavelength scales
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Quantized Nonlinear Thouless Pumping
• Hall effect of triplons in a dimerized quantum magnet
• Observation of strong backscattering in valley-Hall photonic topological interface modes
• Topological one-way large-area waveguide states in magnetic photonic crystals
• Dirac magnons in honeycomb ferromagnets
• Reprogrammable plasmonic topological insulators with ultrafast control
• Extremal transmission and beating effect of acoustic wave in two-dimensional sonic crystal
• Controlling mass and energy diffusion with metamaterials
• Large effective magnetic fields from chiral phonons in rare-earth halides
• Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene
• Measurement of a topological edge invariant in a microwave network
• Topological Insulators by Topology Optimization
• A perspective on topological nanophotonics: current status and future challenges
• Bulk-edge correspondence for topological photonic continua
• Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields
• Hybrid topological photonic crystals
• Observation of unidirectional soliton-like edge states in nonlinear Floquet topological insulators
• Optical isolation with nonlinear topological photonics
• Quantized Fractional Thouless Pumping of Solitons
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• Topological metasurface: From passive toward active and beyond
• Tuning the Berry curvature in 2D Perovskite
• Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• PTD Symmetry Protected Scattering Anomaly in Optics
• Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
• The Emergence of Topological Nodal Points in Photonic Crystal with Mirror Symmetry
• Topological theory of non-Hermitian photonic systems
• Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity
• Observation of Antichiral Edge States in a Circuit Lattice
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Non-reciprocal quantum interactions and devices via autonomous feed-forward
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Photonic ${\mathbb{Z}}_2$ topological Anderson insulators
• A topological photonic ring-resonator for on-chip channel filters
• Topology-Enhanced Nonreciprocal Scattering and Photon Absorption in a Waveguide
• Topological photonics: fundamental concepts, recent developments, and future directions
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Higher-order topological insulators in hyperbolic lattices
• Fano resonance from a one-dimensional topological photonic crystal
• Topological Angular Momentum and Radiative Heat Transport in Closed Orbits
• The Existence of Topological Edge States in Honeycomb Plasmonic Lattices
• Experimental realization of chiral Landau levels in two-dimensional Dirac cone systems with inhomogeneous effective mass
• The Nature of Topological Protection in Spin and Valley Hall Insulators
• Large-area quantum-spin-Hall waveguide states in a three-layer topological photonic crystal heterostructure
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Topological supermodes in photonic crystal fiber
• Tuning Topological Phase Transitions in Hexagonal Photonic Lattices Made of Triangular Rods
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Multifrequency and multimode topological waveguides in a Stampfli-triangle photonic crystal with large valley Chern numbers
• An operator-based approach to topological photonics
• Berry bands and pseudo-spin of topological photonic phases
• Valley-dependent Corner States in Honeycomb Photonic Crystal without Inversion Symmetry
• Nonreciprocal and non-Hermitian material response inspired by semiconductor transistors
• Cubic 3D Chern photonic insulators with orientable large Chern vectors
• Topological slow light via coupling chiral edge modes with flat bands
• A group theoretical route to deterministic Weyl points in chiral photonic lattices
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
• Topological phonon modes in filamentous structures
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Mathematical theory for topological photonic materials in one dimension
• Classifying topology in photonic heterostructures with gapless environments
• Conical diffraction and the dispersion surface of hyperbolic metamaterials
• Unidirectional Maxwellian Spin Waves
• Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices
• Chiral current circulation and $\mathcal{P}\mathcal{T}$ symmetry in a trimer of oscillators
• Topological effects of phonons in GaN and AlxGa1-xN: A potential perspective for tuning phonon transport
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Photonic modal circulator using temporal refractive-index modulation with spatial inversion symmetry
• Topological phase in plasma physics
• Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum
• Robust Topological Terahertz Circuits using Semiconductors
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Time-dependent high-contrast subwavelength resonators
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Hybrid topological magnon-phonon modes in honeycomb and kagome lattices
• On-chip unidirectional waveguiding for surface acoustic waves along a defect line in a triangular lattice
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Section Chern number for a 3D photonic crystal and the bulk-edge correspondence
• The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas
• Topological photonic Su-Schrieffer-Heeger-type coupler
• Chern Invariants of Topological Continua; a Self-Consistent Nonlocal Hydrodynamic Model
• Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model
• Optical properties of honeycomb photonic structures
• Single-mode lasing based on PT-breaking of two-dimensional photonic higher-order topological insulator
• Polaritonic Quantum Matter
• Response to polarization and weak topology in Chern insulators
• Evidence of Magnon-Mediated Orbital Magnetism in a Quasi-2D Topological Magnon Insulator
• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Slow wave and truly rainbow trapping in one-way terahertz waveguide
• Topological transitions and Anderson localization of light in disordered atomic arrays
• Topological Phenomena in Trapped Ion Systems
• On the Role of Symmetries in the Theory of Photonic Crystals
• Topological spin-plasma waves
• Microwave photonic crystals as an experimental realization of a combined honeycomb-kagome lattice
• Robust acoustic pulling using chiral surface waves
• Higher-order topological heat conduction on a lattice for detection of corner states
• Coherent control of topological states in an integrated waveguide lattice
• Observing 0D subwavelength-localized modes at ~100 THz protected by weak topology
• Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces
• Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
• Period-doubled Floquet Solitons
• High Transmission in 120-degree Sharp Bends of Inversion-symmetric and Inversion-asymmetric Photonic Crystal Waveguides
• Topological light guiding and trapping via shifted photonic crystal interfaces
• Topology in shallow-water waves: A spectral flow perspective
• Topological Edge and Corner States in Biphenylene Network
• Polariton vortex Chern insulator
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Berry curvature for coupled waves of magnons and electromagnetic waves
• Quadrature protection of squeezed states in a one-dimensional photonic topological insulator
• Quantized Hall drift in a frequency-encoded photonic Chern insulator
• Electromagnetic Nonreciprocity in a Magnetized Plasma Circulator
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Synthetic gauge potential and effective magnetic field in a Raman medium undergoing molecular modulation
• Effective Floquet model for minimally twisted bilayer graphene
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Zak Phase Induced Topological Nonreciprocity
• Static synthetic gauge field control of double optomechanically induced transparency in a closed-contour interaction scheme
• Topological Materials for Near-Field Radiative Heat Transfer
• Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems
• Transmission properties of time-dependent one-dimensional metamaterials
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Bulk-edge correspondence for unbounded Dirac-Landau operators
• Quantum limits on the time-bandwidth product of an optical resonator
• Negative Thermal Hall Conductance in Two-Dimer Shastry-Sutherland Model with π-flux Dirac Triplon
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Topological Flat Band and Parity-Time Symmetry in a Honeycomb Lattice of Coupled Resonant Optical Waveguides
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Topological edge states in photonic Floquet insulator with unpaired Dirac cones
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Discrete Approximation of Topologically Protected Modes in Magneto-Optical Media
• Electric field induced thermal Hall effect of triplons in the quantum dimer magnets $X$CuCl${}_3$ ($X=$ Tl, K)
• Probing the Topological Anderson Transition in Quasiperiodic Photonic Lattices via Chiral Displacement and Wavelength Tuning
• Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays
• Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices
• Dirac equation in curved spacetime: the role of local Fermi velocity
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Topological Corner Modes by Composite Wannier States in Glide-Symmetric Photonic Crystal
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Robust unidirectional transport in a one-dimensional metacrystal with long-range hopping
• Large-scale free-space photonic circuits in two dimensions
• Small mode volume topological photonic states in one-dimensional lattices with dipole--quadrupole interactions
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation
• Visualization of Photonic Band Structures via Far-field Measurements in SiNx Photonic Crystal Slabs
• Geometry and Topological photonics
• Double Dirac cones in band structures of periodic Schrödinger operators
• Light-Matter interactions in Hofstadter lattice with the next-nearest neighbor couplings
• Topological Frenkel Exciton-Polaritons in One-Dimensional Lattices of Strongly Coupled Cavities
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Light propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws
• Sorting and Routing Topologically Protected Edge States by their Valleys
• Spectroscopy and topological properties of a Haldane light system
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Signature of edge states in resonant wave scattering
• Enhanced Directional Quantum Emission by Tunable Topological Doubly-Resonant Cavities
• Cavity-induced backscattering in a two-dimensional photonic topological system
• Mode Delocalization in Disordered Photonic Chern Insulator
• Linear Response Theory: A Modern Analytic-Algebraic Approach
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Design of a room-temperature topological exciton-polariton laser in a ZnO/TiO${}_2$-photonic crystal slab
• Polariton Chern Bands in 2D Photonic Crystals Beyond Dirac Cones
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Edge States with Hidden Topology in Spinner Lattices
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Classifying bulk-edge anomalies in the Dirac Hamiltonian
• Spin and valley polarized one-way Klein tunneling in photonic topological insulators
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Quantized dynamics in closed quantum systems
• Single-shot measurement of photonic topological invariant
• Topological invariants and topological charges in photonic systems
• Inverse design of dual-band valley-Hall topological photonic crystals with arbitrary pseudospin states
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
• Photonic Nambu-Goldstone bosons
• Non-hermitian topology and entanglement in an optomechanical superlattice
• Topological phase transition in anti-symmetric Lotka-Volterra doublet chain
• Self-induced nonreciprocity from asymmetric photonic topological insulators
• Spectral Invariants of the Magnetic Dirichlet-to-Neumann Map on Riemannian Manifolds
• A Hermitian bypass to the non-Hermitian quantum theory
• Photonic analogue of quantum spin Hall effect
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Frequency Domain Berry Curvature Effect on Time Refraction
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Edge states and the Valley Hall Effect
• Controlling scattering of light through topological transitions in all-dielectric metasurfaces
• Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics
• Constructing qubit edge states by inverse-designing the electromagnetic environment
• Non-Abelian gauge field optics in the time domain
• Direct visualization of topological transitions and higher-order topological states in photonic metasurfaces
• Topological Pseudospin Hall Effect and Multi-frequency Corner Modes in Kagome-based Lattices
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
• Extremely broadband topological surface states in a photonic topological metamaterials
• Multiple topological phases of magnons induced by Dzyaloshinskii-Moriya and pseudodipolar anisotropic exchange interactions in Kagome ferromagnets
• Dirac points in helically structured 1D photonic crystals
• Estimation of the number of negative eigenvalues of magnetic Schrödinger operators in a strip
• Polarization-dependent topology in quantum emitter chains
• Engineering the Bogoliubov Modes through Geometry and Interaction: From Collective Edge Modes to Flat-band Excitations
• Topological Invariant for Bosonic Bogoliubov-de Gennes Systems with Disorder
• Transport properties of photonic topological insulators based on microring resonator array
• Nanoimprinted topological laser in the visible
• Fine Structures of Berry Curvature and Unquantized Valley Chern Numbers in Valley Photonic Crystals